数据结构与算法13-前、后、中序、层次遍历代码框架

前、后、中序遍历的递归和迭代代码框架

前：根左右
后：左右根
中：左根右

递归版本对于三种方法具有一致性：

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def preorderTraversal(self, root):
        """
        :type root: TreeNode
        :rtype: List[int]
        """
        res = []
        def helper(proot):
            if proot is None:
                return
            res.append(proot.val)  # 移动这个append-"根"即可
            left = helper(proot.left)
            right = helper(proot.right)
        helper(root)
        return res

迭代方法各异，但前、后序相似，中序单独考虑

1. 前序

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def preorderTraversal(self, root):
        """
        :type root: TreeNode
        :rtype: List[int]
        """
        res = []  # 里面放val
        if root is None:
            return res
             
        stack = [root] # 先进后出,所以右先进，这样右后出。

        while stack:
            node = stack.pop()
            res.append(node.val)
            if node.right is not None:
                stack.append(node.right)
            if node.left is not None:
                stack.append(node.left)

        return res

2. 后序（"左右根"加反转）

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def postorderTraversal(self, root):
        """
        :type root: TreeNode
        :rtype: List[int]
        """
        res = []  # 里面放val
        if root is None:
            return res
             
        stack = [root]

        while stack:
            node = stack.pop()       
            if node.left is not None:  # left、right顺序和前序相反
                stack.append(node.left)
            if node.right is not None:
                stack.append(node.right)
            res.append(node.val)  # 左右根

        return res[::-1]  # 反转

3. 中序

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def inorderTraversal(self, root):
        """
        :type root: TreeNode
        :rtype: List[int]
        """
        res = []
        if root is None:
            return res
        stack = []
        cur = root
        while stack or cur:
            while cur:  # 把当前节点及其左节点、左节点的左节点...放入stack
                stack.append(cur)
                cur = cur.left
            cur = stack.pop()
            res.append(cur.val)  # 取出最后一个左节点，并将其值放入res
            cur = cur.right  # 取一次右节点
        return res

所有方法：
时间复杂度：访问每个节点恰好一次，时间复杂度为 $O(N)$ ，其中 $N$ 是节点的个数，也就是树的大小。
空间复杂度：取决于树的结构，最坏情况存储整棵树，因此空间复杂度是 $O(N)$。

汇总

# 二叉树节点类
class TreeNode(object):
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

class Solution(object):
    def preorder(self, root):
        # 二叉树的前序遍历-递归
        res = []
        def helper(root):
            if root is None:
                return
            res.append(root.val)  # 中、后序移动此行即可
            left = helper(root.left)
            right = helper(root.right)
        helper(root)
        return res
    
    
    def preorder_list(self, root):
        # 二叉树的前序遍历-非递归
        res = []
        stack = [root]
        if root is None:
            return res
        while stack:
            tmp = stack.pop()
            res.append(tmp.val)
            if tmp.right is not None:
                stack.append(tmp.right)
            if tmp.left is not None:
                stack.append(tmp.left)            
        return res
    
    
    def lastorder_list(self, root):
        # 二叉树的后序遍历-非递归
        # 左右根 加 反转
        res = []
        stack = [root]
        if root is None:
            return res
        while stack:
            tmp = stack.pop()
            if tmp.left is not None:
                stack.append(tmp.left)
            if tmp.right is not None:
                stack.append(tmp.right)
            res.append(tmp.val)
        return res[::-1]
    
    
    def midorder_list(self, root):
        # 二叉树的中序遍历-非递归
        # 特殊一点
        # 左 根 右
        # 所以要先把最左边的放进去，使用cur游标来实现
        res = []
        stack = []
        cur = root
        if root is None:
            return res
        while stack or cur:
            while cur:
                stack.append(cur)
                cur = cur.left
            cur = stack.pop()
            res.append(cur.val)
            cur = cur.right
        return res
    
    
    def hier_simple(self, root):
        # 二叉树的层次遍历-简单版
        res = []
        queue = [root]
        if root is None:
            return res
        while queue:
            tmp = queue.pop(0)
            res.append(tmp.val)
            if tmp.left is not None:
                queue.append(tmp.left)
            if tmp.right is not None:
                queue.append(tmp.right)
        return res
    
    
    def hier_comple(self, root):
        # 二叉树的层次遍历-复杂版
        res = []
        queue = [root]
        if root is None:
            return res
        while queue:
            tmp_list = []
            length = len(queue)
            for i in range(length):
                # 将目前queue中的节点全部吐到tmp_list中，相当于每一行的节点都单独吐到tmp_list中
                # 但又要保证新加入的节点不被吐出，所以固定住原来的queue的长度，只吐原来queue中所存在的节点
                tmp = queue.pop(0)
                tmp_list.append(tmp.val)
                if tmp.left is not None:
                    queue.append(tmp.left)
                if tmp.right is not None:
                    queue.append(tmp.right)
            res.append(tmp_list[:])
        return res